AP Calculus AB - Derivatives Flashcards
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| 7809644322 | Derivative of sin(x) | cosu du |  | 0 |
| 7809644323 | Derivative of cos(x) | -sinu du |  | 1 |
| 7809644324 | Derivative of tan(x) | sec^2u du |  | 2 |
| 7809644325 | Derivative of csc(x) | -cscucotu du |  | 3 |
| 7809644326 | Derivative of sec(x) | secutanu du |  | 4 |
| 7809644327 | Derivative of cot(x) | -csc^2u du |  | 5 |
| 7809644328 | Derivative of arcsin(x) | du/sqrt(1-u^2) |  | 6 |
| 7809644329 | Derivative of arccos(x) | -du/sqrt(1-u^2) |  | 7 |
| 7809644330 | Derivative of arctan(x) | du/(1+u^2) |  | 8 |
| 7809644331 | Derivative of arccsc(x) | -du/abs(u)sqrt(u^2-1) |  | 9 |
| 7809644332 | Derivative of arcsec(x) | du/abs(u)sqrt(u^2-1) |  | 10 |
| 7809644333 | Derivative of arccot(x) | -du/(1+u^2) |  | 11 |
| 7809644334 | Derivative of e^x | e^u du |  | 12 |
| 7809644335 | Derivative of a^x | (a^u) ln(a) du | 13 | |
| 7809644336 | Derivative of ln(x) | du/u |  | 14 |
| 7809644337 | Derivative of log(x) -- (base of a) | du/(u ln(a) ) | 15 | |
| 7809644338 | Outside Inside(F(g(x))) | F'(g(x)) g'(x) | 16 | |
| 7809644339 | Quotient Rule | Bot dervTop - top dervBtm/btm^2 | 17 | |
| 7809644340 | Product Rule | 1st derv2nd + 2nd derv1st | 18 | |
| 7809644341 | Mean Value Theorem | f'(c) = (f(b) - f(a))/ (b - a) | 19 | |
| 7809644342 | Vertical Tangents | Set denominator of Derivative equal to 0 | 20 | |
| 7809644343 | Horizontal Tangents | Set numerator of derivative equal to 0 | 21 | |
| 7809644344 | Find the rate of change, in km/hr, of the distance between the two ships when x = 4 km and y = 3 km | 1. r^2=x^2+y^2 2. 2rdr/dt=2xdx/dt+2ydy/dt 3. 2rdr/dt=2xdx/dt+2ydy/dt Defined at know points 4. dr/dt=4(-15) + 3(10)/5 5. All equals -6km/hr | 22 |